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We extend the inventory lot-size model in this paper to allow for products to deteriorate at variable rates, and demand is characterized by any log concave function of time that fulfils relatively mild criteria. Partial backlogging is possible with this model. The backlogging rate is a time-dependent, exponentially declining function provided by a parameter. We show that not only does the optimal replacement schedule exist, but that it is also unique. We also show that the inventory system's overall cost is a convex function of the number of replenishments. As a result, identifying a local minimum simplifies the search for the best number of replenishments. Finally, a numerical example is given to demonstrate the findings. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to introduce and investigate a novel subclass of analytic functions in the open unit disk by generalizing the Srivastava-Attiya operator. So by using the generalization we have introduced a subclass of analytic function with negative coefficients in the unit disk. We have referred to the previous studies that used the Sirvastava-Attiya operator and generalized it, explained the functions of the class 퓐 and the basic definitions that included this paper. We used some important lemmas from previous studies to prove our results, and we obtained some important geometric properties of the analytical functions. We proved the theorem of growth and destortion, and we showed the cofficient bound, extreme points of the functions in this class, in addition to the radii of the starlike, convex and close-to-convex functions of order 휑. Finally, we defined the 훼 −neighborhood and showed the relationship between the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ (γ , ρ , l , σ) and the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ , ω (γ , ρ , l , σ). [ABSTRACT FROM AUTHOR]

The paper is focused on solution of the kinematic limit analysis problem arising in geotechnical stability assessment. This problem may be classified as conic optimization and for its solution, the Augmented Lagrangian method with adaptive penalty is proposed to enforce equality constraints. The corresponding inner problem leads to the minimization of a convex quadratic function on a closed convex feasible set defined by separable cones and it is solved by projected gradients with spectral step-lengths. The efficiency of the suggested solver is demonstrated on a strip-footing benchmark problem. [ABSTRACT FROM AUTHOR]

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The purpose of this paper is to investigate the duality for optimal control problems with higher-order differential inclusions. Using locally adjoint mappings and the discretization method, we derive the conditions of optimality for a boundary-value problem with higher-order differential inclusions. This method connects a duality relation problem to a continuous concerning problem. Then, thanks to the dual operations of addition and infimal convolution of convex functions, we obtain duality results. In general, the construction of the duality problem with the assistance of discrete and discrete approximation problems necessitates a significant amount of effort to comprehend the computational aspects. Finally, we show that the optimal solutions to the primal convex and dual concave problems are the same. [ABSTRACT FROM AUTHOR]

The effectiveness of stochastic gradient methods strongly depends on a suitable selection of the hyperparameters which define them. Particularly, in the context of large-scale optimization problems often arising in machine learning applications, to properly fix both the learning rate and the mini-batch size in the definition of the stochastic directions is crucial for obtaining fast and efficient learning procedures. In a recent paper [1], the authors propose to define these hyperparameters by combining an adaptive subsampling strategy and a line search scheme. The aim of this work is to adapt this idea to both the stochastic gradient algorithm with momentum and the AdaM method in order to exploit the good numerical behaviour of the momentum-like stochastic gradient methods and the automatic technique to select the hyperparameters discussed in [1]. An extensive numerical experimentation carried out on convex functions, with different data sets, highlights that such combined hyperparameters technique makes the tuning of the hyperparameters computationally less expensive than the selection of suitable constant learning rate and mini-batch size and this is significant from the perspective of GreenAI. Furthermore, the proposed versions of the stochastic gradient method with momentum and AdaM have promising convergence behaviour compared to the original counterparts. [ABSTRACT FROM AUTHOR]

The paper proposes a model recovery anti-windup (MRAW) scheme for linear time-invariant and discrete-time systems under magnitude and rate saturation. The method is a modified, discrete-time counterpart of the algorithm presented in [4]. As it is usual in the MRAW framework the AW compensator contains the exact copy of the plant in order that the ideal (unsaturated) behavior can be preserved in the states. The compensator is a controller that aims to push the plant towards this intended behavior. The design of this control action can be reduced to a construction of a stabilizing state feedback acting on the saturated plant. In [4] this feedback is a linear one, which is designed by convex optimization by enlarging the ellipsoidal approximation of the invariant domain. This paper presents a different, set-theoretic approach, which is based on the precise construction of the maximal control invariant set. The proposed control is a nonlinear one generated by point wise convex optimization. [ABSTRACT FROM PUBLISHER]

The paper presents one important and interesting property of strictly convex functions. On the base of previously proved properties of these functions, we can generalize some global-geometric conclusions, without the even assumption of their differentiability, and also point out some geometric characteristics of the sets of all solutions of parametric optimization problems. Two specific nonlinear parametric optimizations of nonlinear problems -- the minimization and the maximization problems -- exist for them. They express a pair of dual optimization problems. The set of all optimal points has an important geometric interpretation. This paper connects the proved properties of a specific case and a geometric sense. [ABSTRACT FROM AUTHOR]

In the present paper, we consider and investigate a certain class of close-to-convex functions that defined in the unit disk, U = {z : |z| <1}, which denotes as Re{eiα zf'(z)/f(z)-f(-z)} > δ where |α| < π, cos (α) > δ and 0 ≤ δ < 1. Furthermore, we obtain preliminary result for bound f'(z) and determine result for radius of convexity. [ABSTRACT FROM AUTHOR]

In this paper, we present convex hull formulations for a mixed-integer, multilinear term/function (MIMF) that features products of multiple continuous and binary variables. We develop two equivalent convex relaxations of an MIMF and study their polyhedral properties in their corresponding higher-dimensional spaces. We numerically observe that the proposed formulations consistently perform better than state-of-the-art relaxation approaches. [ABSTRACT FROM AUTHOR]

In this paper, we established some new integral inequalities of Hadamard-type for co-ordinated convex functions by using a new integral identity and fairly elementary analysis. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new integral inequalities for co-ordinated m --convex functions by using a new integral identity and basic definitions. We also give some reduced results by selecting special value of parameter m. [ABSTRACT FROM AUTHOR]

In this paper, firstly a new integral equality is proved and based on this equality some new integral inequalities of Hadamard type are given for differentiable Geometric convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m- convex functions via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

This paper examines the estimation of the best weighted approximation and (co)convex functions with varying degrees of polynomial order. There are some situations in which the estimation of the best approximation is not well equipped to deal with the (co)convex and unconstrained polynomial (COCUNP) approximation and the reduction of the control of the rate errors of approximation. The weighted Ditzian-Totik moduli of smoothness (DTMS) and Lebesgue Stieltjes integral are employed to prove. The developed estimate is able to priority unconstrained approximation. [ABSTRACT FROM AUTHOR]

The Hermite-Hadamard type inequality has been extended to some classes of convex functions and composite convex functions. In this paper, we refine the definition of composite-ɸ−1 convex function and definition of m-convex function to define the composite-ɸ−1m-convex functions. From the definition, we obtain some inequalities related to GA-m-convexity, HA-m-convexity, p-m-convexity and LogExp m-convexity. Next, k-composite-ɸ−1m-convex function is defined. Some inequalities of Hermite-Hadamard type for composite-ɸ−1m-convex functions and k-composite-ɸ−1m-convex functions are obtained. From the inequalities obtained, we provide some applications for GG, AG, HA and HH convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we established new inequalities of Hermite-Hadamard-Fejér type for Riemann-Liouville and conformable fractional integrals. [ABSTRACT FROM AUTHOR]

In this paper, we define (h, m) --convex functions on Δ = [a, b] x [x, d] and obtain some properties of this new class of functions. We also prove a new generalization of Hadamard inequality on the co-ordinates. [ABSTRACT FROM AUTHOR]

In this paper, we consider the class Kα* of the functions of the form f(z) = z+a2z2+... which are analytic univalent in the disc D = {z:|z|<1} such that Reα(z2f"(z))′/g′(z)+(zf′(z))′/g;(z)>0 where g ∈ C. This paper focuses on the functional |a2a4-a32| for a function belonging to Kα* is obtained. [ABSTRACT FROM AUTHOR]

In the paper one focuses on a mathematical problem, which is to be formulated in case of treatment of a class of structural problems, in order to properly represent the behavior of the structure, like, for example, in case of mechanical non-linearity of the material. The analytical formulation is presented allowing to identify a set of functions enjoying some special properties, whose combination allows to achieve the problem solution. [ABSTRACT FROM AUTHOR]

For bistatic sonar, the weak signal of target is often buried by the side lobes of strong direct blast after pulse compression. A method is proposed in this paper to suppress the side lobes of matched filter output. The basic idea is to design an FIR filter at the output of matched filter, so that to minimize the ISL (Integrated Side lobe Level), while keeping the main lobe unchanged. The optimal solution is achieved utilizing the convex optimization method. In numerical simulation, the performance of the method is compared with conventional matched filter plus Hamming window methods. The performance is improved 30dB with output gain unchanged simultaneously. The method is also used to design a close-in side lobe-free filter. The close-in side lobe level could achieve-80dB in the simulation. [ABSTRACT FROM PUBLISHER]

Convex optimization techniques are widely used in the design and analysis of variety of problems especially in communications and signal processing. Many communication problems can either be defined as or be converted into convex optimization problems. Convex optimization makes the analysis and numerical solutions much easier. In this paper, a convex optimization survey is presented. It introduces the recent progress in convex optimization algorithms which are used in digital communications and signal processing applications. The goal of this paper is to give an overview of basic concepts of convex sets, functions and convex optimization problems. Hence, engineering problems using modern convex optimization can be recognized and formulated. Multi-Input-Multi-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) problems are discussed in more details. As a proposed work, a special problem is discussed. Formulation of this problem as a convex problem and its solution is proposed. [ABSTRACT FROM PUBLISHER]

This paper introduces a new algorithm for passivity enforcement of linear lumped macromodels in scattering form. As typical in most state of the art passivity enforcement methods, we start with an initial non-passive macromodel obtained by a Vector Fitting process, and we perturb its parameters to make it passive. The proposed scheme is based on a convex formulation of both passivity constraints and objective function for accuracy preservation, thus allowing a formal proof of convergence to the unique optimal passive macromodel. This is a distinctive feature that differentiates the new scheme with respect to most state of the art methods, which either do not guarantee convergence or are not able to provide the most accurate solution. The presented algorithm can thus be safely used for those cases for which existing techniques fail. We illustrate the advantages of proposed method on a few benchmarks. [ABSTRACT FROM PUBLISHER]

In this paper, we consider Path-Based incremental target level algorithm for a type of nondifferentiable optimization in a Hilbert space. We prove that the problem has solutions when the constraint set is bounded, and the sequence generated in this way is weakly convergence. [ABSTRACT FROM PUBLISHER]

Investigating positivity of polynomials over the complex unit disc is a relevant problem in electrical and computer engineering. This paper provides two sufficient and necessary conditions for solving this problem via linear matrix inequalities (LMIs). These conditions are obtained by exploiting trigonometric transformations, a key tool for the representation of polynomials, and results from the theory of positive polynomials. Some numerical examples illustrate the proposed conditions. [ABSTRACT FROM PUBLISHER]

In this paper we propose an algorithm to achieve hard delay constraints in OFDMA systems. The resource scheduler has to ensure that delay deadlines of the packets get achieved and the resources are also not under utilized. This is a very difficult task since the channel and packet arrival in user queues are time varying in nature. The instantaneous decisions of scheduler depend on current as well as future channel and packet arrival considerations. In this paper we represent hard delay deadlines of packets in the form of various constraints. We then develop a constrained optimization problem and propose an efficient algorithm. This algorithm allocates subcarriers and powers to different users in such a way that the objective of sum rate maximization and hard delay constraint achievement are simultaneously attained. [ABSTRACT FROM PUBLISHER]

The object of this paper is to obtain the estimate for second Hankel determinant | a 2 a 2 − a 3 2 | of Ma-Minda starlike and convex functions. Also obtain the estimates for | h 1 h 3 − h 2 2 | of the functions associated with z f (z) . [ABSTRACT FROM AUTHOR]

In this paper the functions F(z) which are q–valent starlike and convex function of order γ, also ϑ–spirallike of order γ within the open unit disk Λ, a few interesting enough conditions concerning coefficient inequalities for positive subcategory of regular and q–valent functions for F(z) are discussed. Many special instances and consequences of those coefficient inequalities are also considered. [ABSTRACT FROM AUTHOR]

In this paper we establish some new integral inequalities analogous to the Opial inequality by using the proved lemma and some classical inequalities for convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we establish Hermite-Hadamard type inequalities for Riemann- Liouville integrals via (α, m)-geometrically convex funtions. [ABSTRACT FROM AUTHOR]

In this paper, new integral inequalities of Hermite-Hadamard type are developed for n-times differentiable quasi-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, some new Hermite-Hadamard type inequalities involving fractional integrals for s-convex functions in the second sense are derived. [ABSTRACT FROM AUTHOR]

in this paper, we gave the new general identity for differentiable function. As a result of this identity some new and general fractional integral inequalities for differentiable GA-convex functions are obtained. [ABSTRACT FROM AUTHOR]

The paper addresses the nonconvex nonsmooth optimization problem with the cost function and equality and inequality constraints given by d.c. functions. The original problem is reduced to a problem without constraints with the help of the exact penalization theory. After that, the penalized problem is represented as a d.c. minimization problem without constraints, for which the new mathematical tools under the form of global optimality conditions (GOCs) are developed. The GOCs reduce the nonconvex problem in question to a family of convex (linearized with respect to the basic nonconvexities) problems. On the base of the proposed theory we develop numerical methods of local and global search for the problem in question. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of interpolation between locally convex spaces, the real method, and to present some elementary results in this setting. This represents a generalization from the Banach spaces framework to the locally convex spaces sequentially complete one, where the operators acting on them are locally bounded. [ABSTRACT FROM AUTHOR]

In this paper, it is defined the operator GA-convex functions for continuous functions of self-adjoint operators in Hilbert spaces. And then it is obtained some new Hermite-Hadamard type inequalities for this class of functions. [ABSTRACT FROM AUTHOR]

In this study, by using convex functions, we first establish new refinements of Hermite-Hadamard-Fejer type inequalities via Riemann-Liouville fractional integral operators. The results given in this paper provide generalization of several inequalities obtained in earlier studies. [ABSTRACT FROM AUTHOR]

In this paper we proved some new Hadamard-type inequalities for h-convex functions. [ABSTRACT FROM AUTHOR]

Distributed compressed sensing exploits information redundancy, inbuilt in multi-signal ensembles with interas well as intra-signal correlations, to reconstruct undersampled signals. In this paper we revisit this problem, albeit from a different perspective, of taking streaming data, from several correlated sources, as input to a real time system which, without any a priori information, incrementally learns and admits each source into the system. [ABSTRACT FROM PUBLISHER]

In high dimensional classification problem, two stage method, reducing the dimension of predictor first and then applying the classification method, is a natural solution and has been widely used in many fields. The consistency of the two stage method is an important issue, since errors induced by dimension reduction method inevitably have impacts on the following classification method. As an effective method for classification problem, boosting has been widely used in practice. In this paper, we study the consistency of two stage method-dimension reduction based boosting algorithm (briefly DRB) for classification problem. Theoretical results show that Lipschitz condition on the base learner is required to guarantee the consistency of DRB. This theoretical findings provide useful guideline for application. [ABSTRACT FROM PUBLISHER]

In real world, there are many uncertain conditions which cannot be absolutely pre-determined or controlled by the decision maker. Then, by the empirical experience in the market behavior, there are no fixed carrying cost rate, interest paid rate and interest earned rate. In this paper, we will extend Chen et al. [1] model with fuzzification in the carrying cost rate, interest paid rate and interest earned rate, simultaneously, based on the triangular fuzzy numbers to fit the real world. Then, in our new fuzzy model, we will discuss some conditions or theorems to find the optimal solution for the total variable cost per unit time in fuzzy sense. Moreover, we will take some examples to illustrate our proposed model. [ABSTRACT FROM PUBLISHER]

One of the major objectives of cognitive radar is to form a dynamic closed feedback loop to adapt the spectrum of transmit waveforms to avoid certain interference. In this paper, we build an automatic closed-loop cognitive radar to support experimental study of the radar system in real-world situations. Convex optimization is applied to jointly design sounding waveforms and the matched filters with spectral power suppressed in arbitrary bands and with low correlation sidelobes as well. Target localization is demonstrated under strong interferences. Experimental results are provided to evaluate the performance of the cognitive radar system. [ABSTRACT FROM PUBLISHER]

This paper studies average waiting time analysis of opportunistic access in multi-channel cognitive radio networks with a single secondary user and multiple primary users by applying the M/G/1 preemptive priority queueing scheme. By employing convex optimization tool, the secondary user finds the optimal way to distribute the packets to all channels in the system. For sensitive delay network, we proposed an algorithm to distribute the secondary user's packets to the only group of channels which satisfy the delay constraint. Simulation are used to validate the results, and simulation results demonstrate a high degree of accuracy for the derived expressions. Results indicate that the performance of the secondary user depends on the data traffic characteristics of the primary users and also the delay constraint of the secondary user. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce the regularized Newton method for multiobjective optimization. The method does not scalarize the original multiobjective optimization problem. For any vector convex function, with a compact level set, the regularized Newton method generates a sequence that converges to the optimal points from any starting point. Moreover the regularized Newton method does not require strong convexity property in the entire space. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a distributed optimization algorithm that minimizes the energy consumption of lossless data gathering wireless sensor networks by allocating variable transmit power and data compression/transmission rate to each sensor node. Using the Lagrange duality, we decompose the convex energy consumption minimization problem into subproblems, which can be solved by the sensor nodes distributively. The convergence of the iterative algorithm is demonstrated by the simulations. [ABSTRACT FROM PUBLISHER]

In this paper the problem of optimization of near-convex functions which can be represented as a sum of strongly convex and bounded functions is addressed. We have noted that in several optimization problems in area of image processing cost functions follow this model. Here we present an algorithm how to minimize such functions using randomized smoothing technique. The technique is an attractive theoretical justification of global optimization properties of SPSA-like algorithms. We present bounds on estimates error after finite number of steps, asymptotic bounds, bounds on estimates' variance and show how the algorithm presented can robustly optimize a function with many similar local minima. [ABSTRACT FROM PUBLISHER]

This paper presents two methodologies for analyzing the H2 guaranteed cost performance of a discrete-time LTI system with norm-bounded structured uncertainty. The first methodology is based on semi-definite programming and the second methodology is based on smooth nonlinear convex optimization in which each function evaluation requires the solution of one discrete algebraic Riccati equation. The two methods are then compared in terms of their speed and accuracy. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the model reduction for Markov chain models. The goal is to obtain a low-rank approximation to the original Markov transition matrix. A nuclear-norm regularized optimization problem is proposed for this purpose, in which the Kullback-Leibler divergence rate is used to measure the similarity between two Markov chains, and the nuclear norm is used to approximate the rank function. An efficient iterative optimization algorithm is developed to compute the solution to the regularized problem. The effectiveness of this approach is demonstrated via numerical examples. [ABSTRACT FROM PUBLISHER]

We consider the problem of energy-optimal time allocation of a series of point-to-point motions. When performing a series of point-to-point motions, the individual execution time of each motion is, in many cases, free to choose as long as the total execution time of the series of point-to-point motions is not exceeded. This paper presents an algorithm to compute the time allocated to each motion in a series of point-to-point motions in an energy-optimal way. The algorithm is demonstrated on a technology demonstration test facility at Flanders' Mechatronics Technology Centre. [ABSTRACT FROM PUBLISHER]

Isermann (1978) established that every efficient solution of optimization problem is properly efficient if the objective functions are linear and feasible set is polyhedral. Choo (1984) proved this result when the objective functions are linear fractional and the feasible set is a compact polyhedron. Chew and Choo (1984) established that every efficient solution of optimization problem which satisfies the following boundedness condition is properly efficient if all the objective functions and constraint functions are pseudolinear. A feasible point χ∈Χ is said to satisfy the boundedness condition if the set {Pi(χ*,χ)Pj(χ*,χ):fi(χ)i(χ*),fj(χ)>fj(χ*),1≤i,j≤κ} is bounded above, where pi is a proportional function corresponding to fi,i = 1,2,3,.........κ. Gulati and Islam (1990) have shown that the above result still holds if we take the objective functions to be pseudolinear, constraint functions to be quasiconvex and certain constraint qualification is satisfied. In this paper we show that every efficient solution that satisfies the above boundedness condition and generalized constraint qualification, is properly efficient if all the objective functions and constraint functions defined on a convex set are semilocally pseudolinear and their right differentials at that efficient solution are convex. [ABSTRACT FROM AUTHOR]